Algebra: Sets, Symbols, and the Language of Thought

Algebra: Sets, Symbols, and the Language of Thought

by John Tabak
     
 

ISBN-10: 0816049548

ISBN-13: 9780816049547

Pub. Date: 06/28/2004

Publisher: Facts on File, Incorporated

The History of Mathematics is a fascinating survey of the development of math through discovery, innovation, collaboration, and experimentation. The set presents a compelling overview of myriad aspects of mathematics using understandable language and appealing line illustrations and photographs. Algebra is a thorough examination not only of how and why this branch of

Overview

The History of Mathematics is a fascinating survey of the development of math through discovery, innovation, collaboration, and experimentation. The set presents a compelling overview of myriad aspects of mathematics using understandable language and appealing line illustrations and photographs. Algebra is a thorough examination not only of how and why this branch of mathematics arose and flourished in different cultures at different times but also of its useful applications in science and in society. Author John Tabak pinpoints the foundations of algebra more than 4,000 years ago in Mesopotamia and traces its progress in other ancient civilizations around the world, including the Hindu, Greek, and Arabic cultures, and at different points in history. Mostly rhetorical in its early forms, algebra in the symbolic form that we use today was formalized in the 17th century. Over the past three centuries, algebra has taken two diverging paths: one toward increasingly higher levels of abstraction, the other toward more concrete computational methods. Tabak explores algebra as an indispensable part of every branch of mathematics and a widely utilized tool in scientific and engineering research. Algebra includes an index, a chronology of notable events, a glossary of terms, a helpful list of Internet resources, and an array of historical and current print sources. Keyed to current principles and standards in teaching math, The History of Mathematics set is essential for young readers who require information on relevant topics in mathematics.

Product Details

ISBN-13:
9780816049547
Publisher:
Facts on File, Incorporated
Publication date:
06/28/2004
Series:
Facts on File History of Mathematics Series
Pages:
240
Product dimensions:
6.28(w) x 9.34(h) x 0.81(d)
Age Range:
14 - 17 Years

Related Subjects

Table of Contents

Introduction: Algebra as Languagexi
1The First Algebras1
Mesopotamia: The Beginnings of Algebra2
Mesopotamians and Second-Degree Equations5
The Mesopotamians and Indeterminate Equations7
Clay Tablets and Electronic Calculators8
Egyptian Algebra10
Chinese Algebra12
Rhetorical Algebra16
2Greek Algebra18
The Discovery of the Pythagoreans19
The Incommensurability of [radical]224
Geometric Algebra25
Algebra Made Visible27
Diophantus of Alexandria31
3Algebra from India to Northern Africa35
Brahmagupta and the New Algebra38
Mahavira42
Bhaskara and the End of an Era44
Islamic Mathematics46
Poetry and Algebra47
Al-Khwarizmi and a New Concept of Algebra50
A Problem and a Solution53
Omar Khayyam, Islamic Algebra at Its Best54
Leonardo of Pisa59
4Algebra as a Theory of Equations60
The New Algorithms63
Algebra as a Tool in Science69
Francois Viete, Algebra as a Symbolic Language71
Thomas Harriot75
Albert Girard and the Fundamental Theorem of Algebra79
Further Attempts at a Proof83
Using Polynomials88
5Algebra in Geometry and Analysis91
Rene Descartes95
Descartes on Multiplication98
Pierre de Fermat102
Fermat's Last Theorem105
The New Approach106
6The Search for New Structures110
Niels Henrik Abel112
Evariste Galois114
Galois Theory and the Doubling of the Cube117
Doubling the Cube with a Straightedge and Compass Is Impossible120
The Solution of Algebraic Equations122
Group Theory in Chemistry127
7The Laws of Thought130
Aristotle130
Gottfried Leibniz133
George Boole and the Laws of Thought137
Boolean Algebra141
Aristotle and Boole144
Refining and Extending Boolean Algebra146
Boolean Algebra and Computers149
8The Theory of Matrices and Determinants153
Early Ideas155
Spectral Theory159
The Theory of Matrices166
Matrix Multiplication172
A Computational Application of Matrix Algebra175
Matrices in Ring Theory177
Chronology179
Glossary197
Further Reading203
Index213

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